THE QUANTITATIVE METHOD in BIOLOGY Published by the University of Manchester At

PUBLICATIONS OF THE UNIVERSITY OF MANCHESTER BIOLOGICAL SERIES No. II THE QUANTITATIVE METHOD IN BIOLOGY Published by the University of Manchester at THE UNIVERSITY PRESS (H. M. McKechnie, Secretary) 12 Lime Grove, Oxford Road, MANCHESTER LONGMANS, GREEN & CO. London : 39 Paternoster Row, E.C.4 New York : 443-449 Fourth Avenue and Thirtieth Street Chicago : Prairie Avenue and Twenty-fifth Street Bombay : 8 Hornby Road Calcutta : 6 Old Court House Street Madras : 167 Mount Road THE QUANTITATIVE METHOD IN BIOLOGY BY Julius MacLeod, Dr Nat. Sc. Professor of Botany in the University of Ghent WITH 27 FIGURES 9& l^' MANCHESTER : AT THE UNIVERSITY PRESS 12 LIME GROVE, OXFORD ROAD LONGMANS, GREEN & CO. LONDON, NEW YORK, BOMBAY, ETC 1919 PUBLICATIONS OF THE UNIVERSITY OF MANCHESTER No. CXX M3^ All rights reserved PREFACE In Physics, Chemistry and Mineralogy the properties of the objects are measured and expressed by means of figures called constants. A constant is independent of any theory : it is the exact expression of a fact. The constants are in reality the material by means of which theories are built up, the explana- tion of the observed facts is found and the road opened for new discoveries. In Botany and Zoology, on the contrary, the properties (characters) of the living things are usually described by means of terms. We say that a given object is long or short, broad or narrow, oblong or oval, etc. Much progress would be rendered possible if such terms as long, broad, short, etc., were replaced by figures. This would be simple enough if the properties of animals and plants were invariable. Unfortunately these properties are almost always variable, not only within the limits of one species, but also among the children of the same parents and even among the progeny of one parent.^ Variability has been hitherto the great obstacle which has rendered impossible the general use of quantitative data (figures) in Biological Sciences. The object of the present book is to describe a method by which biological constants may be established. In the first two chapters I have expounded certain theoretical views about the notion of species and variation. Those views afford us a guide for the discovery of the primordia (simple or elementary properties or characters) which are to be measured in order to find constants. The constants themselves are, however, entirely independent of any theory and of any ^ Parthenogenesis, apogamy, asexual multiplication in animals and plants. V VI PREFACE calculation whatsoever. Each constant is a direct expression of an observed fact. I have been asked several times in what way the described method was to be applied to the investigation of certain given properties of certain animals or plants. My answer is that in each peculiar case a preliminary investigation is required in order to find the primordia which are to be measured and the way in which the measurements are to be carried out. This preliminary work may be a long one. For example, I began in December 19 14 the study of the British species of the genus Mnium (Acrocarpic Mosses). I spent two months on the preparatory work before I had found a dozen of the primordia and established their exact definition and the method of measuring them. In a similar way it took me in 1916 about three months to determine exactly twenty-five primordia of the fertile stem of the Grasses. In 1907 I began the measurement of thirty-eight primordia of the species of the genus Carabus after a preparatory investigation of the simple properties of the Coleoptera and other insects which lasted several years. Such work is, I think, an excellent school for the biologist, because he becomes aware of the vagueness of many of our notions. As soon as we require to make measurements, we feel again and again compelled to replace approxi- mations by exact definitions. It may be hoped that the preparatory work under consideration will become easier in proportion as the number of examples investigated becomes greater. The work needed for the measurement of the primordia of animals and plants is rather lengthy, but biologists ought not to shrink from the idea of undertaking such a laborious task. It may be recalled that the physicists, the chemists and the mineralogists have already collected hundreds of thousands of constants at the cost of tremendous toil. They have per- severed in spite of numerous difficulties. For example, in order to establish exactly the constants (atomic weight, specific gravity, melting-point, etc.) of a given metal, a pure specimen PREFACE vii must be provided, and the preparation of a pure specimen may last several months. Moreover, many figures obtained by the measurement of inorganic objects are variable according to the external conditions, in the same way as the dimensions and other properties of living beings. For instance, the density of a substance varies to given according temperature ; pressure has an influence on the etc. in order boiling-point ; Therefore, to establish constants, certain conventions have been made ; this renders the task still more laborious and delicate. Biologists should not allow themselves to be discouraged by the prospect of " such work " should remember what lengthy ; they always the students of inorganic nature have already carried out. When an index of refraction, a coefficient of expansion or a given angle of a crystal has been exactly measured, work and perseverance find their reward, because a precise notion has been acquired once for all. In Biology, on the contrary, especially in the descriptive (systematic) part of Zoology and Botany,! numerous objects have been described again and as new contradiction and hesitation ; again ; prevail everywhere an enormous amount of labour has been wasted. We should follow the example given by physicists, chemists and mineralo- of gists. Otherwise it may be feared that the work, like that Penelope, will go on indefinitely. It may be remarked that the present book is NOT in reality a treatise on mathematical biology : mathematical notions (Part VI.) are used only in order to find the primordia and the methods of measuring them. We may hope that when a sufficient number of constants have been collected the power- ful machinery of mathematical science will become applicable to biological problems. I have, in conclusion, the pleasant duty of acknowledging the assistance received from various friends. To Professor F. E. Weiss, who has kindly read through the manuscript and has made numerous corrections in the language, and to Professor W. H. Lang, in whose laboratory 1 See on Embryology, § 50. viii PREFACE I have been working for more than three years, I am indebted for the most cordial assistance. Both of them have given me bibliographical information of a most useful character. I beg Professor G. Unwin, who kindly helped me with the language, to accept my most sincere thanks. To Professor Niels Bohr, Copenhagen, I am indebted for useful remarks about the mathematical part. Finally, I have to express my great obligation to Mr W. D. Evans, M.A., who has read through the manuscript and proofs of the mathematical part and who has assisted me in various ways. Julius MacLeod. The University, Manchester. 2isi Dece?7iber 1918. CONTENTS PAGE PREFACE V LIST OF ILLUSTRATIONS xii PART I THE NOTION OF SPECIES IS A CHEMICAL NOTION . i The Living Substance of each Specific Form is a Mixture of a Number of Chemical Entities—Each Specific Mixture differs from all others by at least one Entity— Chemical Classification of Plants and Animals— and Series of Entities— — — Groups — Chemical— Glycerides Proteins Natural Mixtures Bioproteins Biotic and Abiotic Chemical Properties— Heredity—Individual Variation—Mutation—Lamarckism PART II THE OBSERVABLE PROPERTIES OF EACH SPECIES ARE. PRODUCED BY REACTIONS OF ITS LIVING SUB- STANCE 9 — Possible and Observable Properties Range of Possibilities—Plasticity— Variants—Complexity—Monotypic and Complex Species—Subspecies —Pure Lines—Bud-Variation—Bud-Species—Continuous and Dis- continuous Variation—Adaptation—Accommodation—Variation under Cultivation—Latent Properties PART III QUANTITATIVE METHOD AND PRIMORDIA . .25 Summary of Parts I. and II. —Use of the Quantitative Method in the and Classification of — — — Description— — Species Linnaeus— Latreille— Bertil- lonage — Biometry— Quantitative— Variation Quetelet Variation Curves Galton Weldon Pearson — Davenport—Biometrika—Appli- cation of the Quantitative Method on the Study of Hybridization— Mendel—The Mendelian Experiments in Relation to the Notion of Species—Simple and Compound Properties—Primordia—Observable Properties and Hereditary Factors—Segregation (Dissociation) of into Compound Properties Primordia by Hybridization, Plasticity, Gradation and in the Course of Individual Development—The Mendelian Method of is — describing—Hybrids applicable on the Description of Species Phyllotaxis Quantitative Investigation of Physiological Functions X CONTENTS PART IV PAOB THE PRIMORDIA 51 The Adult State is a State of Equilibrium—Each Primordium repre- sents a State of Equilibrium—Individual Adaptation (Accommodation) is —Classification of the Primordia Equilibrium— — — with reference to their Development Sensitive —Period Correlation Independence of the Primordia—Psedogenesis Measurement of a State of Equilibrium— Curves of Development— Leading Property—Variation in Embryology PART V ATTEMPT AT A CLASSIFICATION OF THE PRIMORDIA 66 Numerous Primordia mentioned in existing Descriptive Literature— Classification of the Primordia

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